Question

The mean throwing distance of a football for a Luis, a high school freshman quarterback, is 50 yards, with a standard deviation of three yards. The team coach tells Luis to adjust his grip to get more distance. The coach records the distances for 35 throws. For the 35 throws, Luis’s mean distance was 54 yards. The coach thought the different grip helped Luis throw farther than 50 yards. Conduct a hypothesis test using a preset α = 0.01. Assume the throw distances for footballs are normal.

a. Determine what type of test this is: A, B or C? A) Single population mean with standard deviation known B) Single population mean with standard deviation not known C) Single population proportion

b. Identify the null hypothesis, A, B,C or D? Identify the alternative hypothesis, A, B,C or D ? A) mu greater or equal than 50 B) mu greater than 50 C) mu less or equal than 50 D) mu less than 50

c. Find the p-value to nearest whole number

d. State your conclusion, A, B, or C? A. Can't reject null. There is not sufficient evidence from this sample data to show that Luis’s mean throwing distance is greater than 50 yards. B. Reject null. There is sufficient evidence from this sample data to show that Luis’s mean throwing distance is greater than 50 yards. C. no conclusion

Answer 1

Given:

Sample size = n = 35

 Sample mean =

Standard deviation = = 3

a) The type of test this i Single population mean with standard deviation known.

Answer - option a

b) Claim: The coach thought the different grip helped Luis throw farther than 50 yards.

Level of significance =

Hypothesis test :

The null and alternative hypothesis is

H0 :   = 50

Ha : > 50

Answer - option B

c) Test statistic is

z = ( - ) / / n

= (54-50) / 3 / √35

= 7.89

Test statistic = 7.89

p-value :

p-value = P( Z > 7.89) = 0.0000 ... ( from z table)

p-value = 0.0000

d) conclusion :

Since p-value = 0.0000 < 0.01 level of significance , we reject null hypothesis H0.

The correct option is:

Reject null. There is sufficient evidence from this sample data to show that Luis’s mean throwing distance is greater than 50 yards.

Answer - option B